A sentence like "The man has white hair and beard" is totally acceptable in languages without countable/uncountable nouns or articles, and languages where modifiers follow the head noun (barring gender agreement issues).
But in English, both "The man has white [hair and _ _ beard]," and "The man has [white hair] and [a _ beard]" feel inaccurate, if not ungrammatical. Only "The man has [white hair] and [a white beard]" feels right.
As "He has dark [hair and _ eyes]" seems fine, it appears the presence of the article preceding the countable noun prevents it from being modified by the overt 'white'.
I'm looking for more information on conjunction reduction between constituents that require an article and ones that don't, specifically in cases where adjectives are involved in the reduction. Is this a phenomenon in English? Is there a better way to describe it, or somewhere I could read more about this specific topic?